if b/2 < -2.326207163052239e+115

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   48.8
2. Using strategy rm
   48.8
3. Applied add-exp-log to get
   \[\frac{\left(-b/2\right) + \color{red}{\sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\left(-b/2\right) + \color{blue}{e^{\log \left(\sqrt{{b/2}^2 - a \cdot c}\right)}}}{a}\]
   49.8
4. Applied taylor to get
   \[\frac{\left(-b/2\right) + e^{\log \left(\sqrt{{b/2}^2 - a \cdot c}\right)}}{a} \leadsto \frac{\left(-b/2\right) + e^{\log \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}{a}\]
   16.6
5. Taylor expanded around -inf to get
   \[\frac{\left(-b/2\right) + e^{\log \color{red}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}}{a} \leadsto \frac{\left(-b/2\right) + e^{\log \color{blue}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}}{a}\]
   16.6
6. Applied simplify to get
   \[\frac{\left(-b/2\right) + e^{\log \left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}{a} \leadsto \frac{\frac{\frac{1}{2} \cdot c}{\frac{b/2}{a}} - \left(b/2 - \left(-b/2\right)\right)}{a}\]
   1.4

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7. Applied final simplification

if -2.326207163052239e+115 < b/2 < -1.9116038778178358e-274

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   8.9

if -1.9116038778178358e-274 < b/2 < 4.449432714488087e+57

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   28.9
2. Using strategy rm
   28.9
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   29.1
4. Applied associate-/l/ to get
   \[\color{red}{\frac{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}} \leadsto \color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{a \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)}}\]
   33.7
5. Applied taylor to get
   \[\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{a \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)} \leadsto \frac{c \cdot a}{a \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)}\]
   22.0
6. Taylor expanded around inf to get
   \[\frac{\color{red}{c \cdot a}}{a \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)} \leadsto \frac{\color{blue}{c \cdot a}}{a \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)}\]
   22.0
7. Applied simplify to get
   \[\frac{c \cdot a}{a \cdot \left(\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}\right)} \leadsto \frac{\frac{c}{1}}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}\]
   10.2

---

8. Applied final simplification
9. Applied simplify to get
   \[\color{red}{\frac{\frac{c}{1}}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}} \leadsto \color{blue}{\frac{c}{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - c \cdot a}}}\]
   10.2

if 4.449432714488087e+57 < b/2

1. Started with
   \[\frac{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}{a}\]
   58.3
2. Using strategy rm
   58.3
3. Applied flip-+ to get
   \[\frac{\color{red}{\left(-b/2\right) + \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\color{blue}{\frac{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}}{a}\]
   58.3
4. Applied simplify to get
   \[\frac{\frac{\color{red}{{\left(-b/2\right)}^2 - {\left(\sqrt{{b/2}^2 - a \cdot c}\right)}^2}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{\color{blue}{a \cdot c}}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a}\]
   32.4
5. Applied taylor to get
   \[\frac{\frac{a \cdot c}{\left(-b/2\right) - \sqrt{{b/2}^2 - a \cdot c}}}{a} \leadsto \frac{\frac{a \cdot c}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}\]
   15.2
6. Taylor expanded around inf to get
   \[\frac{\frac{a \cdot c}{\color{red}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}}{a} \leadsto \frac{\frac{a \cdot c}{\color{blue}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}}{a}\]
   15.2
7. Applied simplify to get
   \[\color{red}{\frac{\frac{a \cdot c}{\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - 2 \cdot b/2}}{a}} \leadsto \color{blue}{\frac{c}{\left(\frac{1}{2} \cdot c\right) \cdot \frac{a}{b/2} - 2 \cdot b/2}}\]
   1.6